India, denied victory on day four by the tail-end resistance of Pat Cummins, were forced to wait nearly two-and-a-half hours for play to begin due to rain at the Melbourne Cricket Ground but when the weather cleared their bowlers wrapped up the Australia innings for 261 in 22 minutes.
In his second over seamer Jasprit Bumrah had Cummins edge to Cheteshwar Pujara, who took a sharp, low catch in the slips to remove the seam bowler for a personal high score of 63.
Paceman Ishant Sharma then sealed the result when he had Nathan Lyon edge behind for seven when attempting to slog the ball.
The wicket triggered bear hugs and backslaps among the Indian side as travelling fans in the sparse crowd roared with joy.
Having dominated with bat and ball throughout the one-sided Boxing Day clash, Virat Kohli’s side will head to the Sydney Cricket Ground with a genuine belief they can become the first Indian team to win a series Down Under.
Resuming on 258 for eight, 141 runs short of victory, Australia’s best hope was for rain to wash out the final day but the morning showers merely delayed the inevitable.
They had been set a daunting victory target of 399 shortly before lunch on day four, and crumbled after India’s pacemen attacked the stumps with cold-blooded assurance.
The pride of Cummins and Lyon allowed Australia to limp into day five but the match had slipped away from the hosts on the morning of day three, the rampaging Bumrah taking 6-33 to rout Paine’s side for 151 and carve out a first-innings lead of 292.
Australia will head into the final match pondering a litany of problems.
They may wonder whether their defiant win in the second test in Perth was merely a false dawn rather than a turning point for a rebuilding team.